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Contrary to what the desciption says it's not only damage from monsters that fails this, but any damage (absorbed or not)

Turn on your combat log to show Stuff that has happened to you, and choose a tanky companion.

Protector Yi is rather charge happy and tends to add loads and loads of mobs, so I personally prefer Chao the Voice, who doesn't have nearly the survivability but tanks just as well.

Some short tips:

The Gai-Cho Earthtalkers should be avoided at any cost. The cast an instant earthquake that is pretty much unvaoidable.

The Yaungol have a charge, that they only use on targets outside of the minimum range.The safest way to do this quest is to throw explosives from "The Enemy of My Enemy... Is Still My Enemy!" at the three groups up the slope to the village. It takes some time but it's safe.

Cheng Bo! was the hardest one for me personally. He has two instantly respawning adds, one of them an Earthtalker. So if you don't have CC you should wait for somemone else to come along and simply let them kill him, after you tagged him once and ran away.

The others are pretty standard. Just be careful to run out of stuff and don't add additional packs.